Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 653 · 40 sums

The method (Split into easy parts): (a + b)² = a² + 2ab + b². (a − b)² = a² − 2ab + b². (a + b)(a − b) = a² − b²; so a² − b² = (a + b)(a − b). a² + b² = (a + b)² − 2ab = (a − b)² + 2ab.

1. 1.If a + b = 5 and ab = 6, what is a² + b²?
2. 2.Use (a + b)² = a² + 2ab + b² to find 41².
3. 3.Use a² − b² = (a + b)(a − b) to find 51² − 21².
4. 4.Use (a + b)² = a² + 2ab + b² to find 42².
5. 5.If a − b = 5 and ab = 24, what is a² + b²?
6. 6.Use (a + b)(a − b) = a² − b² to find 72 × 68.
7. 7.Find the value of x² − 2xy + y² when x = 9 and y = 6.
8. 8.Use (a + b)² = a² + 2ab + b² to find 74².
9. 9.Use a² − b² = (a + b)(a − b) to find 73² − 23².
10. 10.Use (a + b)(a − b) = a² − b² to find 101 × 99.
11. 11.Find the value of x² + 2xy + y² when x = 7 and y = 6.
12. 12.Use (a + b)² = a² + 2ab + b² to find 86².
13. 13.Find the value of x² − 2xy + y² when x = 6 and y = 5.
14. 14.Use a² − b² = (a + b)(a − b) to find 20² − 9².
15. 15.Use a² − b² = (a + b)(a − b) to find 68² − 62².
16. 16.Use (a + b)² = a² + 2ab + b² to find 26².
17. 17.Use (a + b)² = a² + 2ab + b² to find 62².
18. 18.Use (a − b)² = a² − 2ab + b² to find 83².
19. 19.Use a² − b² = (a + b)(a − b) to find 83² − 44².
20. 20.Use (a − b)² = a² − 2ab + b² to find 95².
21. 21.Use (a + b)² = a² + 2ab + b² to find 92².
22. 22.If a + b = 9 and ab = 18, what is a² + b²?
23. 23.Use a² − b² = (a + b)(a − b) to find 68² − 24².
24. 24.Use a² − b² = (a + b)(a − b) to find 36² − 7².
25. 25.If a − b = 3 and ab = 28, what is a² + b²?
26. 26.Use a² − b² = (a + b)(a − b) to find 41² − 28².
27. 27.Find the value of x² − y² when x = 5 and y = 1.
28. 28.If a + b = 7 and ab = 6, what is a² + b²?
29. 29.Use (a + b)² = a² + 2ab + b² to find 11².
30. 30.Use (a + b)(a − b) = a² − b² to find 93 × 87.
31. 31.Use (a + b)² = a² + 2ab + b² to find 12².
32. 32.Use a² − b² = (a + b)(a − b) to find 96² − 43².
33. 33.Use a² − b² = (a + b)(a − b) to find 52² − 6².
34. 34.Use (a − b)² = a² − 2ab + b² to find 51².
35. 35.Use (a + b)² = a² + 2ab + b² to find 51².
36. 36.Use (a + b)(a − b) = a² − b² to find 29 × 11.
37. 37.Find the value of x² + 2xy + y² when x = 3 and y = 2.
38. 38.Use (a + b)² = a² + 2ab + b² to find 19².
39. 39.Use (a − b)² = a² − 2ab + b² to find 74².
40. 40.Use (a + b)² = a² + 2ab + b² to find 57².

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